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A circular disc rolls on a horizontal Iloor without slipping and the centre of the disc moves with a uniform velocity $v$. Which of the following values of the velocily at a point on the rim of the disc can have?
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The correct answers are:
$v$, $2 v$, Zero
Consider the rolling motion of a circular disc as shown in the adjacent diagram. Velocity of point of contact $(P)$ is $v_{P}=v-\omega R=v-v=0$
$$
[\because v=\omega R]
$$
velocity of point ${ }^{\prime} S^{\prime}, v_{S}=v+\omega R=2 V$
velocity of centre ' $O^{\prime}, v_{0}=v-\omega(0)=V$ Velocity of a point ' $T$ at distance $R$ from $P$ is $V_{T}=\omega R=\mathrm{O}_{V}$
Thus possible velocities are $v, 2 v$ and $0 .$
$$
[\because v=\omega R]
$$
velocity of point ${ }^{\prime} S^{\prime}, v_{S}=v+\omega R=2 V$
velocity of centre ' $O^{\prime}, v_{0}=v-\omega(0)=V$ Velocity of a point ' $T$ at distance $R$ from $P$ is $V_{T}=\omega R=\mathrm{O}_{V}$
Thus possible velocities are $v, 2 v$ and $0 .$
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